Modeling of Unsteady‐Flow Water Temperatures

Abstract

A mathematical model is presented to simulate water temperatures of one‐dimensional unsteady flows in a river‐lake system having time‐varying lateral inflows and several cross‐sectional changes along its length. In the hydraulic part initial steady state conditions are computed by numerically integrating the gradually‐varied flow equation using the fourth‐order Runge‐Kutta method and the unsteady flow conditions by integrating the one‐dimensional Saint Venant equations using an implicit finite difference method. An upwind implicit finite difference scheme is used to solve the partial differential equation governing the water temperature of unsteady flows. Comparison of the computed water temperatures with those measured on the Columbia and Kootenay Rivers show good agreement.